J. Agric. Food Chem. 2004, 52, 2137−2146
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Simplified Enzymatic High-Performance Anion Exchange Chromatographic Determination of Total Fructans in Food and Pet FoodsLimitations and Measurement Uncertainty PAUL STO¨ BER,* SYLVIE BEÄ NET,
AND
CLAUDIA HISCHENHUBER
Nestle´ Research Centre, Vers-chez-les-Blanc, 1000 Lausanne 26, Switzerland
A simplified method to determine total fructans in food and pet food has been developed and validated. It follows the principle of AOAC method 997.08, i.e., high-performance anion exchange chromatographic (HPAEC) determination of total fructose released from fructans (Ff) and total glucose released from fructans (Gf) after enzymatic fructan hydrolysis. Unlike AOAC method 997.08, calculation of total fructans is based on the determination of Ff alone. This is motivated by the inherent difficulty to accurately determine low amounts of Gf since many food and pet food products contain other sources of total glucose (e.g., starch and sucrose). In this case, a correction factor g can be used (1.05 by default) to take into account the theoretical contribution of Gf. At levels >5% of total fructans and in commercial fructan ingredients, both Ff and Gf can and should be accurately determined; hence, no correction factor g is required. The method is suitable to quantify total fructans in various food and pet food products at concentrations g0.2% providing that the product does not contain other significant sources of total fructose such as free fructose or sucrose. Recovery rates in commercial fructan ingredients and in selected food and pet food ranged from 97 to 102%. As part of a measurement uncertainty estimation study, individual contributions to the total uncertainty (u) of the total fructan content were identified and quantified by using the validation data available. As a result, a correlation between the sucrose content and the total uncertainty of the total fructan content was established allowing us to define a limit of quantitation as a function of the sucrose content. One can conclude that this method is limited to food products where the sucrose content does not exceed about three times the total fructan content. Despite this limitation, which is inherent to any total fructan method based on the same approach, this procedure represents an excellent compromise with regard to accuracy, applicability, and convenience. KEYWORDS: Fructans; inulin; fructanase; inulinase; high-performance anion exchange chromatography; measurement uncertainty
INTRODUCTION
Fructans are oligomeric and polymeric carbohydrates composed of β-linked fructose monomers. According to the type of linkage [β(2f1) or β(2f6)], one distinguishes between inulin or levan type fructans. Inulin type fructans are the storage carbohydrates of many plants of the Compositae family, in particular of chicory root (Cichorium intybus). Graminan type fructans of mixed β(2f1) and β(2f6) structure are found in low concentrations in grains of several grasses and cereals, in particular in rye and wheat. Inulin is composed of polydisperse linear chains of β(2f1)linked fructose (F) moieties, generally bearing a terminal glucose (G) unit. The molecular structure of inulin type fructans is therefore usually referred to as GFn (n ) 3 to ∼60). In inulin from chicory, Fm fructans (without terminal glucose) coexist * To whom correspondence should be addressed. E-mail: Paul.Stoeber@ rdls.nestle.com.
with their GFn homologues. Fructooligosaccharides (FOS) or oligofructose refer to the low molecular weight fraction of inulin (n ) 2-9). Because of the lack of the enzyme fructanase in the human digestive system, fructans are considered as nondigestible oligosaccharides. For this reason, they are classified as soluble dietary fiber from a nutritional and legal point of view in most countries worldwide. In addition, they are claimed to have a beneficial impact on the gut flora (prebiotic effect) (1). Bacterial species thought to be selectively promoted through the consumption of prebiotics are in particular Bifido bacteria and Lactobacillus strains. For both reasons, commercial inulin and FOS preparations are used as functional ingredients and added to an increasing number of food products (2). Typically, the amount used in a food application is 5 g/100 g and commercial fructan ingredients, Gf was taken into account (see formulas in ref 7) and the total fructan content was calculated according to eq 1.
g)
Ff + Gf Ff
(4)
Table 3 shows the g factors for selected fructan ingredients. Ideally, this factor should be determined for each specific ingredient. However, the analysis of most commercial fructan ingredients refined from chicory root showed typically an Ff/ Gf ratio close to 20:1, which corresponds to a g factor of 1.05. Therefore, a suitable correction factor g to be used by default appears to be 1.05. It should be borne in mind that g may actually be very different from 1.05, especially in the case of Actilight, which is exclusively composed of the three short chain fructans GF2 to GF4. Limit of Quantitation. Given the contribution of sucrose to the amount of total fructose, the question of the limit of quantitation has to be addressed in a different way for sucrosefree products and for sucrose-containing products. For sucrosefree products (milk powder, pet food), spiking experiments demonstrated (based on a minimum recovery of 90%, results not shown) that total fructans can be accurately determined using the proposed method down to at least 0.2 g/100 g. For products containing sucrose, the limit of quantitation is directly dependent on the amount of sucrose. The relationship between the amount of sucrose and the limit of quantitation is discussed in the next paragraph. Measurement Uncertainty (MU). The MU of the proposed method was estimated based on the approach recommended by
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Table 2. Comparative Analysis under Conditions of AOAC Method 997.08, with and without the R-Glucan Hydrolysis Step with R-glucan hydrolysis step
without R-glucan hydrolysis step
Gfa (g/100 g)
Ff ‚ k (g/100 g)
(Ff + Gf) ‚ k (g/100 g)
Ffa (g/100 g)
Gfa (g/100 g)
Ff ‚ k (g/100 g)
(Ff + Gf) ‚ k (g/100 g)
product
k
Ffa (g/100 g)
milk powder spiked with 5% Raftiline HP whole wheat meal dry dog food with 8% chicory
0.910 0.910
4.95 1.03
0.15 0
4.51 0.94
4.68 0.94
4.73 1.01
0.22 2.87
4.31 0.91
4.51 3.51
0.910
4.31
0.22
3.92
4.12
4.06
1.39
3.69
4.96
a
Mean of duplicate determination.
released from fructans (Ff) is
Table 3. g Factors of Selected Fructan Ingredients product
Ff (g/100 g)
Gf (g/10 g)
g
Raftiline HP Raftilose P95 dried chicory root Actilight P950
101.5 95.3 57.5 69.6
4.18 3.71 5.29 25.4
1.04 1.04 1.09 1.37
u(Ff) x[u(Ftot)2 + u(Ffree)2 + u(S)2] ) Ff S Ftot - Ffree 1.9
(
the ISO and Eurachem Guides (10, 11). It is divided into five steps (Table 4). The aim of a MU estimation study is to determine a standard deviation of uncertainty or standard uncertainty u(y) related to the result of the measurand y. If individual contributions of random and systematic effects (a, b, c, ...) are independent, the total uncertainty is obtained according to the general formula:
u(y) ) y
x[ ] [ ] [ ] 2
2
2
u(a) u(b) u(c) + + +... a b c
(5)
Eventually, the MU should be expressed as a confidence interval or expanded uncertainty U(y) around the result y obtained. We have recently applied this approach to the estimation of the MU of the HPAE chromatographic determination of free and total carbohydrates in soluble coffee (12). Step 1: Description of the Measurement Procedures Flowchart of the Method. Scheme 1 shows the flowchart of the method. Step 2: Specification of the MeasurandsRelationship between the Measurand and the Variables. Combining eqs 2 and 3, the total fructan concentration cf (g/100 g) (without determination of Gf) can be expressed as follows:
(
cf ) k ‚ g ‚ Ftot - Ffree -
S 1.9
)
(6)
and the relative standard uncertainty of the amount of fructose
(7)
)
Accordingly, the relative standard uncertainty of cf can be determined as follows:
x[ ] [ ] [ ] x [ ] [ ] [ x
u(cf) ) cf
u(Ff) 2 u(k) 2 u(g) 2 + + ) k g Ff
u(k) 2 u(g) 2 + + k g
(
)
2
[u(Ftot)2 + u(Ffree)2 + u(S)2] S Ftot - Ffree 1.9 (8)
]
Free carbohydrates (Ffree and S) are determined in the assay A1. For the purpose of MU estimation, the purity of the carbohydrate standard (PST) as well as the recovery of free carbohydrates (Rfree) need to be taken into consideration. Their concentration cfreecarb (g/100 g) is therefore obtained according to the following equation:
cfreecarb )
A1 ‚ mST ‚ V1 ‚ D1 ‚ 100 PST ‚ AST ‚ m ‚ VST ‚ DST Rfree
(9)
where A1 ) peak area of the carbohydrate measured in the sample solution, assay A1; AST ) peak area of the carbohydrate measured in the standard solution; mST (g) ) weight of the carbohydrate in the standard solution, in grams; m (g) ) weight of the test portion, in grams; V1 (mL) ) volume of the sample solution, assay A1; VST (mL) ) volume of the standard solution; D1 ) dilution factor of the sample solution, assay A1; and DST ) dilution factor of the standard solution.
Table 4. Summary of the Procedure for the Estimation of MU step
objective
how to do it
1
description of the measurement procedure
2
specification of the measurand
3
identification of uncertainty sources
4
quantitation of uncertainties
5
combination of uncertainties
Produce a flowchart with a description of all steps to be included in the measurement (analytical) procedure. All conversions (manipulations) should appear separately. Define the measurement model, which is the relationship between the measurand and the variables of the measuring (analytical) procedure. Write the main equation of the analytical method. Identify and show the uncertainty sources for each variable by means of a cause and effect diagram based on the main equation. Quantify the identified uncertainties. Tabulate them in an uncertainty budget table. Combine the uncertainties according to error propagation rules to yield the total uncertainty of the measurand.
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Scheme 1. Flow Chart of the Enzymatic HPAEC Determination of Total Fructans
Scheme 2. Cause and Effect Diagram for the Determination of Free Carbohydrates
The concentration of each carbohydrate (cST) in the mixed standard solution used for calibration is given as:
cST )
mST ‚ PST VST ‚ DST
(10)
Therefore, eq 9 can be simplified to:
cfreecarb )
A1 ‚ cST ‚ V1 ‚ D1 ‚ 100 AST ‚ m ‚ Rfree
(11)
Similarly, the concentrations of total carbohydrates (ctotcarb, fructose, and glucose) determined in assay A2 are obtained according to eq 12:
ctotcarb )
A2 ‚ cST ‚ V1 ‚ V3 ‚ D2 ‚ 100 AST ‚ m ‚ V2 ‚ Rtot
(12)
where A2 ) peak area of the carbohydrate measured in the sample solution, assay A2; V2 (mL) ) volume of the aliquot taken from sample solution, assay A1; V3 (mL) ) volume of the sample solution, assay A2; D2 ) dilution factor of the sample solution, assay A2; and Rtot ) recovery of total carbohydrates. To determine the standard uncertainties of cfree and ctotcarb, individual uncertainty contributions related to each of the variables need to be identified and quantitatively estimated. Step 3: Identification of Uncertainty SourcessCause and Effect Diagram. According to eq 11, the cause and effect diagram can be drawn for the determination of free carbohydrate (Scheme 2). The repeatability of the individual carbohydrate determination is known because samples are analyzed in duplicate. The repeatability takes into account all operations regarding the sample (mass, volume, dilution, injection, peak area, and peak integration). It can therefore be extracted and dealt with separately. It is also suitable to deal with linearity
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Scheme 3. Refined Cause and Effect Diagram for the Determination of Free Carbohydrates
Table 5. Relative Repeatability Standard Deviations RSD(r) of the
Duplicate Determination of Free and Total Carbohydrates as a Function of the Carbohydrate Concentration range (g/100 g) free carbohydrates total galactose total glucose total fructose
10
10% 20%
4% 5%
2.5% 1.5% 1.5% 1.5%
1.5%
2%
0.5%
and repeatability of the peak area of the carbohydrate standard separately. Accordingly, a refined cause and effect diagram can be drawn (Scheme 3). Similarly, a refined cause and effect diagram can be set up for the total carbohydrates assay (not shown). Step 4: Quantitation of Individual Uncertainties. Precision (Repeatability). Using HPAEC-PAD, the repeatability varies with the type of carbohydrate analyzed (mono- or disaccharide), its retention time (larger peaks with increasing retention times), and its concentration. The sample dilution factor and the condition of the working electrode also have an impact of the repeatability. The duplicate results obtained on 114 analysis of different products (23 for total glucose) were statistically analyzed. For free sugars, only a differentiation according to the carbohydrate concentration range has been made, thus neglecting the other influences. For total sugars, a differentiation according to the type of carbohydrate and its concentration range is made. The values of relative standard deviation of repeatability RSD(r) or u(r)/r observed in our laboratory are summarized in Table 5. Trueness. Four different fructan preparations were analyzed according to the proposed method. Results were calculated according to eq 1, that is taking into account the contribution of total glucose (Gf). The results (Table 6) were compared to their theoretical fructan content [The theoretical fructan content was calculated from the free sugar content (determined as part of this method), the moisture content (determined by Karl Fischer), and estimates of ash, proteins, and fat (according to specifications).] to determine the recovery. Recoveries ranging between 97 and 102% were found. To check the recovery in a finished food and in a pet food, a milk powder and a dry dog food (both sucrose-free) product
were spiked with Raftilose P95 and Raftiline ST, respectively. [Milk powder, respectively, 3, 6, and 9%; dog food, 0.25, 0.5, 1.0, 2.5, and 5%. Results were calculated according to eq 2 (not shown).] Again, recoveries between 97.5 and 102.5% were achieved (except for the dog food spiked with 0.25% where the recovery was 92%). We therefore assumed the total fructan recovery R both in fructan ingredients and finished products to be 100 ( 2.5% over the a total fructan range of 0.5-100 g/100 g. To transform this interval into a relative standard deviation of recovery RSD(R), a normal distribution is assumed. Division by 1.96 leads to an RSD(R) of 1.28%. For lower total fructan values (0.25-0.5 g/100 g), the recovery R can be assumed to be 100 ( 8% (rectangular distribution, division by square root of 3, resulting RSD(R) ) 4.62%) [A rectangular (or uniform) distribution around x is assumed if no information of the level of confidence of x is available. All values between x ( tolerance interval are equally likely to be true. A triangular distribution around x is assumed if values close to x are more likely than those close to the limits of the tolerance interval.] Calibration with Mixed Carbohydrate Standard Solution. Three points have to be considered to discuss the uncertainty related to the calibration of the chromatographic system using a mixed carbohydrate standard solution: the repeatability of the carbohydrate standard peak area (integration), the uncertainty linked to the lack of linearity, and the uncertainty of the carbohydrate standard concentration. Repeatability of the Carbohydrate Standard Peak Area (rareaST). Performing HPAEC-PAD analysis of carbohydrates, the electrochemical response (peak area) is subject to variations within a series of injections. Another source of uncertainty is the repeatability of the integration of the peak area. A typical sample series is composed of an injection of the mixed carbohydrate standard solution, followed by up to six sample injections (e.g., three samples in duplicate) and another standard solution. All six sample chromatograms are integrated using the mixed standard preceding the sample series. To quantitatively evaluate the variation of the detector’s response within one series of injections, we monitored the differences in the peak areas of each carbohydrate in two mixed standard solutions in a row, that is separated by six sample injections. Eighteen pairs of mixed standard chromatograms were analyzed in this way, and the relative repeatability standard deviations of the peak areas for each individual carbohydrate
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Table 6. Total Fructan Recovery in Commercial Fructan Preparations fructan content product Raftilose P95a Raftiline HPa Raftiline STb Actilight P950b
Ff Gf (g/100 g) (g/100 g) Ff/Gf 94.8 101.3 89.6 69.6
3.7 4.2 8.2 25.4
25.6 24.2 11.0 2.75
k 0.925 0.905 0.91 0.94
(Ff + Gf) ‚ k theoretical recovery (g/100 g) (g/100 g) (%) 91.1 95.4 89.0 89.3
91.6 95.0 89.7 91.5
97−100 99−102 99 98
a Mean of five determinations in duplicate. b Mean of one determination in duplicate.
Table 7. Carbohydrate Specific Relative Uncertainties Related to the
Calibration carbohydrate
RSD(rareaST) (%)
RSD(linST) (%)
RSD(cST) (%)
galactose glucose sucrose fructose
1.8 1.0 1.7 2.4
2.0 2.0 3.0 3.0
0.8 0.8 0.8 0.8
standard RSD(rareaST) were determined. The RSD(rareaST) values found were 1.0% for glucose and 2.4% for fructose (see Table 7). Uncertainty of Linearity. Calibration is done by injecting a mixed standard solution at one single concentration for each carbohydrate (external one point calibration). It is therefore imperative to check the linearity of the response for each carbohydrate in order to define a suitable concentration working range. As a general tendency, the linear range of the response of carbohydrates on the PAD is relatively limited. At high carbohydrate concentrations, the detector tends to saturate and the response (ratio peak area over concentration) decreases rapidly. To determine the appropriate working range, 10 mixed carbohydrate standard solutions at 10 different carbohydrate concentrations were analyzed and the resulting peak areas for each carbohydrate were recorded. Subsequently, a plot of the ratio of peak area over concentration against the concentration was done. Fructose and sucrose tend to have a “less linear behavior” with PAD than other carbohydrates, that is their response actually very slightly decreases over the whole concentration range analyzed. We defined maximum acceptable relative standard deviation of the ratio peak area over concentration for each carbohydrate standard, RSD(linST). They can be considered as a compromise between acceptable precision and working range, keeping in mind that the calibration model is not perfect. Thus, RSD(linST) values ranging between 2.0 and 3.0% were used as criteria to define the lower and upper limit of the working range (Table 7). At the same time, these values express the uncertainty related to the linear calibration model. Figure 1 shows the plot obtained for fructose. To define the working range while complying with the RSD(linST) previously defined of 3.0%, the three highest fructose standard concentrations had to be discarded. Carbohydrate Concentration in the Mixed Standard Solution (cST). The carbohydrate standard solution is a mixture of the individual carbohydrate standards at the same concentrations (0.04 mg/mL). The same solution is used in the “free” and in the “total” carbohydrate assay. To calculate the uncertainty of the concentrations of the mixed carbohydrate standard solution, the following contributions were taken into account (see eq 10): (i) mST, mass of the carbohydrate standard (100 mg); (ii) PST, purity of the carbohydrate standard (g99%); (iii) VST, volume of the undiluted mixed carbohydrate
Figure 1. PAD response of fructose and linear range defined (dotted
line).
standard solution (100 mL); and (iv) DST, dilution of this solution (dilution factor 25). We have previously demonstrated that the contributions of the determinations of mST and VST are negligible, whereas those of PST and DST are both about 0.6%. Accordingly, the standard uncertainty of cST is approximately:
u(cST) )
x[ ] [ ]
u(PST) 2 u(DST) 2 + ) 0.8 PST DST
(13)
Uncertainty Budget of Calibration with Mixed Carbohydrate Standard Solution. The individual contributions to the relative standard uncertainty related to the calibration with the standard solution are summarized in Table 7. Remaining Biases (Sample Solution and Dilution Factor). The relative uncertainties related to the sample weight m and the sample solution volume V1 have been shown to be negligible. The relative standard uncertainty of an overall dilution factor of 10 (10 mL pipetted into a 100 mL volumetric flask) has been shown to be about 0.45%. Accordingly, the relative standard uncertainty of a dilution factor of 100 (two subsequent dilutions by 10, as generally used in assay A2) is about 0.65%. Combination of Standard UncertaintiessTotal Uncertainty Budget. The total uncertainty budget of the HPAEC determination of free and total carbohydrates is summarized in Table 8 (The dilution factor V3/V2 ‚ D2 applies only to the total carbohydrate assay.). Determination of the MU. The relative standard uncertainty of a free carbohydrate concentration is calculated as follows:
u(cfreecarb) ) cfree carb
x[ ] [ ] [
] [
]
u(cST) 2 u(linST) 2 u(rareaST) u(r) 2 + + + r cST linST rareaST
2
(14)
The relative standard uncertainty of a total carbohydrate concentration is calculated as follows: u(ctotcarb) ctotcarb
)
x[ ] [ ] [ ] [
] [
]
u(cST) 2 u(linST) 2 u(rareaST) 2 u(V3/V2 ‚ D2) u(r) 2 + + + + r cST linST rareaST V3/V2 ‚ D2
2
(15)
Examples. Case Study 1: Sucrose-Free Milk Powder Containing About 3.0% of Fructans. This product is used as a quality
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Table 8. Total Uncertainty Budget of the HPAEC Determination of Free and Total Carbohydrates uncertainty parameter
symbol
value repeatability depends on the concentration
c < 0.2 0.2 < c < 1.0 1.0 < c < 10 c > 10
r
concentration standard linearity peak area standard dilution factor
cST linST rareaST V3/V2 ‚ D2
calibration 0.04 depends on the carbohydrate 100
unit
u(x)
u(x)/x
g/100 g
depends on the concentration
10.0% 4.0% 2.5% 1.5%
mg/mL
0.00033 depends on the carbohydrate 0.636
0.8% depends on the carbohydrate 0.64%
Table 9. Uncertainty Budget of a Total Fructose Content of
Table 10. Uncertainty Budget of a Ff Content of 3.12 g/100 g in Milk
3.24 g/100 g
Powder uncertainty
parameter repeatability: 1.0 < c < 10 calibration: concentration standard linearity peak area standard dilution factor total fructose content
symbol
value
unit
u(x)
r
3.24
g/100 g
0.046
1.5%
cST linST rareaST (V3/V2) ‚ D2 c
0.04 linST rareaST 100 3.24
mg/mL
0.000326
g/100 g
0.64 0.1376
0.8% 3.0% 2.4% 0.64% 4.25%
uncertainty
u(x)/x
uncertainty contribution to Ff
parameter
symbol
value
unit
u(x)
u(x)/x
sucrose free fructose total fructose fructose released from fructans
S Ffree Ftot
0.04 0.09 3.24
g/100 g g/100 g g/100 g
0.0042 0.0097 0.1376
0.14% 0.31% 4.40%
3.12
g/100 g
0.1380
4.42%
Ff
Table 11. Uncertainty Budget of a Total Fructan Content of 3.03 g/100
g in Milk Powder uncertainty
Figure 2. Uncertainty budget of a total fructose content of 3.24 g/100 g.
control (QC) sample in our laboratory. The mean value of eight determinations under intermediate reproducibility conditions was 3.10 g/100 g of total fructans. On the basis of the standard deviation of the mean of the duplicates (0.16 g/100 g), control limits of ( 0.40 g/100 g (multiplication by 2.58) had been defined for its use as QC sample in our laboratory. This experimental control limit was compared to the calculated MU of a determination in duplicate. After analysis, the milk powder is found to contain 0.04 g/100 g of sucrose, 0.09 g/100 g of free fructose, and 3.24 g/100 g of total fructose. Table 9 and Figure 2 summarize the individual contributions and the total standard uncertainty of a total fructose content of 3.24 g/100 g [u(cf)/cf ) 4.25%]. The overall repeatability of the determination, the repeatability of the integration of the external carbohydrate standards, and the uncertainty related to the linear calibration model used account for the major part of the standard uncertainty of cf. Similarly, the total uncertainties determined for free fructose [c ) 0.04 g/100 g, u(c) ) 0.0042, and u(c)/c ) 10.6%] and sucrose [c ) 0.09 g/100 g, u(c) ) 0.0097, and u(c)/c ) 10.7%] were determined. The amount of fructose released from fructans (Ff) is calculated according to eq 6. It is interesting to determine the
parameter
symbol
value
unit
u(x)
u(x)/x
fructose released from fructans correction factor correction factor total fructans (k ‚ g ‚ Ff) recovery (cf > 0.5 g/100 g) total fructans corr. R
Ff k g cf R cfcorr.R
3.12 0.925 1.05 3.03 100 3.03
g/100 g
0.1380 0.0058 0.0058 0.1351 1.28 0.1420
4.42% 0.63% 0.55% 4.47% 1.28% 4.67%
g/100 g % g/100 g
individual contributions of each carbohydrate to Ff. The standard uncertainty related to the determination of total fructose is the only relevant contribution to the standard uncertainty of Ff (Table 10). The total fructan content of the milk powder is calculated according to eq 2: cf ) 3.03 g/100 g (with k ) 0.925 and g ) 1.05). Its standard uncertainty is determined according to eq 8. However, this uncertainty needs to be corrected for the standard uncertainty of the total fructan recovery, and eq 8 becomes
x[ ] [ ] x[ ] x[ ] [ ] u(cfcorr.R) cfcorr.R
u(R) R
)
u(R) R
2
+
2
u(cf) Cf
+
u(k) k
2
+
2
)
u(g) g
2
+
{
}
x[u(Ftot)2 + u(Ffree)2 + u(S)2]
(F
tot
- Ffree -
S 1.9
)
2
(16)
The uncertainty intervals of both the k and the g factor were arbitrarily estimated to be 0.01. To transform these intervals into standard deviations, a rectangular distribution is assumed (division be square root of 3). Accordingly, the following uncertainty budget for a total fructan content of 3.03 g/100 g is obtained (Table 11 and Figure
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Table 13. Uncertainty Budget of a Total Fructan Content of 2.96 g/100
g in an Infant Formula uncertainty parameter fructose released from fructans correction factor water uptake correction factor for Gf total fructans (k ‚ g ‚ Ff) recovery (cf > 0.5 g/100 g) total fructans corr. R
symbol
value
unit
u(x)
u(x)/x
Ff
3.05
g/100 g
0.5379
17.64%
k g cf R cfcorr.R
0.925 1.05 2.96 100 2.96
g/100 g % g/100 g
0.0058 0.0058 0.5230 1.28 0.5245
0.63% 0.55% 17.66% 1.28% 17.71%
Figure 3. Uncertainty budget of a total fructan content of 3.03 g/100 g
(sucrose-free milk powder). Table 12. Uncertainty Budget of a Ff Content of 3.05 g/100 g in an
Infant Formula uncertainty
uncertainty contribution to Ff
parameter
symbol
value
unit
u(x)
u(x)/x
sucrose free fructose total fructose fructose released from fructans
S Ffree Ftot
10.3 0.08 8.55
g/100 g g/100 g g/100 g
0.3964 0.0086 0.3636
13.0% 0.3% 11.9%
3.05
g/100 g
0.5379
Ff
17.64%
Figure 4. Uncertainty budget of a total fructan content of 2.96 g/100 g
3). The standard uncertainty related to the contribution of totalfructose represents the only relevant source of the total uncertainty. The thus determined standard uncertainty has to be multiplied by 2 to obtain the “expanded uncertainty” U, which designs a confidence interval in which the probability to find the “true” value is 95% (Multiplication by 2 has been suggested by the Eurachem guide to transform relative uncertainties into 95% confidence levels.). Accordingly, the result of the total fructan determination in the milk powder should be reported as:
cf ) 3.03 ( 0.28 g/100 g
(17)
This corresponds to an expanded uncertainty of (9% of the actual value. As a conclusion, the calculated expanded uncertainty is about of the same order as the experimental control limit based on the intermediate reproducibility study ((0.40 g/100 g). It appears that the intermediate reproducibility could be used as a fair approximation to estimate the MU of the present method applied to this sample. Case Study 2: Infant Formula Containing 10% Sucrose and 3.0% of Fructans. After analysis, the infant formula is found to contain 10.3 g/100 g of sucrose, 0.08 g/100 g of free fructose, and 8.55 g/100 g of total fructose. The u(c)/c values calculated according to eqs 14 and 15 for these three carbohydrates are 3.85, 10.7, and 4.25%, respectively. As can be seen from Table 12, because of the high amount of sucrose and its contribution to the amount of total fructose, both the contribution of sucrose and the total fructose become major sources of the uncertainty of Ff. The total fructan content of the infant formula is calculated according to eq 2, and its standard uncertainty again is calculated according to eq 16. Accordingly, the following uncertainty budget for a total fructan content of 2.96 g/100 g is obtained (Table 13 and Figure 4). In this case, the determinations of
(sucrose-rich infant formula).
sucrose and total fructose account almost exclusively for the total uncertainty of cf. Accordingly, the result of the total fructan determination in the infant formula containing should be reported as:
cf ) 2.96 ( 1.05 g/100 g
(18)
This corresponds to an expanded uncertainty of (35% of the actual value. Relationship between Total Fructan and Sucrose Content. A simulation of the expanded MU that can be expected at different total fructan levels as a function of the sucrose content was carried out. For this purpose, a product was assumed to contain no free fructose, and a k factor of 0.925 and a g factor of 1.05 were used. A limit of quantitation of total fructans in the presence of sucrose can be deduced if one defines a maximum acceptable expanded MU of the actual value. For instance, assuming an expanded standard uncertainty of (33% of the actual value as a criterion to define the limit of quantitation, a linear relationship between total fructan and sucrose content is obtained (Figure 5). In other words, on the basis of this criterion, the limit of quantitation of total fructans by this method (without taking into account Gf) can be approximated by the following equation:
LoQ (cf) ) 0.3 ‚ sucrose content
(19)
It should be kept in mind that a similar relationship exists in principle for any total fructan method based on the same approach (that is, independent determinations of sucrose and total fructose), even if it obviously also depends on the analytical method used to determine these carbohydrates. CONCLUSION
On the basis of the principle of AOAC method 997.08, a simplified method for the determination of total fructans in food
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Figure 5. Relationship between total fructan and sucrose for a given
expanded uncertainty of ±33% of the total fructan amount.
and pet food has been developed and validated. The method is suitable to quantify total fructans at any concentration g0.2% (without sucrose) in food and pet food products as well as in fructan ingredients (raw materials and preparations). It is important to keep in mind that no distinction is made between inulin and graminan type fructans; in other words, cereal fructans will contribute to the overall amount of fructans determined in a finished product. In the proposed method, the result is based on the determination of Ff alone (fructose released from fructans upon enzymatic hydrolysis) for products containing less than about 5% of total fructans, which covers the vast majority of actual fructan applications in finished food and pet food products. This is justified by the inherent difficulty to accurately determine low amounts of Gf (glucose released from fructans) by difference in most fructan-containing food products. To take into account the theoretical contribution of Gf, the use of a correction factor g is proposed. A suitable correction factor to be used by default is 1.05, which corresponds to a Ff/Gf ratio of 20 as found in most commercially available fructan preparations. The method also allows us to determine precisely g if the fructan ingredient used in the food product analyzed is known and available for analysis. As part of a MU estimation study, the method’s performance criteria have been evaluated. The recovery, both in fructan preparations and in finished food and pet food products, ranged from 97 to 102%. Following the recommendations of the Eurachem guide, all relevant contributions to the total standard uncertainty of the total fructan result have been identified and quantified. With regard to the HPAE chromatographic determination of fructose, glucose, and sucrose, the most relevant sources of the total standard uncertainty are the repeatability of the determination in duplicate (between 1 and 3%), the repeatability of the integration of the external carbohydrate standards (1.0-2.4%), and the uncertainty related to the linear calibration model used (2-3%). However, given that the total fructan result is obtained by difference, the case of products where fructans are the only sources of total fructose to be determined has to be distinguished from that where other carbohydrates contribute to the total fructose amount (mainly sucrose). In products without sucrose, the relative standard uncertainty u(cf)/cf is typically about 4.5% (expanded uncertainty U about (9% of the actual result). Interestingly, the calculated MU for the in-house quality control sample used in our laboratory is of about the same order as the control limit determined based on an intermediate reproducibility study. In products containing sucrose, the MU is directly related to the [fructans to sucrose] ratio. As an approximation, we could
Sto¨ber et al. demonstrate that this method (and in principle any total fructan method based on the same approach) is not appropriate to quantify fructans with reasonable accuracy in products containing an amount of sucrose that is about three times (or more) that of total fructans. To improve the accuracy of the determination of Ff in the presence of significant amounts of sucrose (e.g., in infant formulas), sucrose can be selectively hydrolyzed and the resulting free sugars reduced to sugar alcohols by borohydride prior to the enzymatic fructan hydrolysis step (9). However, the undesired reduction of reducing Fm type fructans in this alternative method is another problem and requires a sound knowledge of the composition of the fructan ingredient to be analyzed (use of correction factor). ACKNOWLEDGMENT
We are grateful to Lionel Spack for fruitful discussions regarding the application of the concept of MU estimation. LITERATURE CITED (1) Gibson, G. R.; Roberfroid, M. B. Dietary modulation of the human colonic microbiotica: Introducing the concept of prebiotics. J. Nutr. 1995, 125, 1401-1412. (2) Roberfroid, M. B.; Van Loo, J.; Gibson, G. R. The bifidogenic nature of chicory inulin and its hydrolysis products. J. Nutr. 1997, 128, 11-19. (3) Shiomi, N.; Onodera, S.; Chatterton, N. J.; Harrison, P. A. Separation of fructooligosaccharide isomers by anion-exchange chromatography. Agric. Biol. Chem. 1991 55 (5), 1427-1428. (4) Durgnat, J.-M.; Martinez, C. Determination of fructooligosaccharides in raw materials and finished products by HPAE-PAD. Semin. Food Anal. 1997, 2, 85-97. (5) Campbell, J. M.; Bauer, L. L.; Fahey-GC, J.; Hogarth, A. J. C. L.; Wolf, B. W.; Hunter, D. E. Selected fructooligosaccharide (1-kestose, nystose, and 1-F-beta-fructo-furanosyl-nystose) composition of foods and feeds. J. Agric. Food Chem. 1997, 45, 3076-3082. (6) Hogarth, A. J. C. L.; Hunter, D. E.; Jacobs, W. A.; Garleb, K. A.; Wolf, B. W. Ion chromatographic determination of three fructooligosaccharide oligomers in prepared and preserved foods. J. Agric. Food Chem. 2000, 48, 5326-5330. (7) Hoebregs, H. Fructans in Foods and Food Products, IonExchange Chromatographic Method: Collaborative Study. J. AOAC Int. 1997, 80 (5), 1029-1037. (8) McCleary, B. V. Importance of enzyme purity and activity in the measurement of total dietary fiber and dietary fiber components. J. AOAC Int. 2000, 83, 997-1005. (9) McCleary, B. V.; Murphy, A.; Mugford, D. C. Measurement of total fructan in foods by enzymatic/spectrophotometric method: collaborative study. J. AOAC Int. 2000, 83 (2), 356-364. (10) Guide to the Expression of Uncertainty in Measurement, 1st ed.; ISO: Geneva, 1993, ISBN 92-6710188-9. (11) Quantifying Uncertainty in Analytical Measurement, 2nd ed.; Ellison, S. L. R. (LGC, GB), Roesslein, M. (EMPA, CH), Williams, A. (GB), Eds.; Eurachem/CITAC, 2000, ISBN 0948926-155. (12) Sto¨ber, P.; Giller, V.; Spack, L.; Prodolliet, J. Estimation of the Measurement Uncertainty of the High-Performance AnionExchange Chromatographic Determination of Carbohydrates in Soluble (Instant) Coffee. J. AOAC Int. Accepted for publication. Received for review July 14, 2003. Revised manuscript received January 7, 2004. Accepted January 29, 2004.
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